The present invention relates generally to methods, systems and technologies that computationally integrate process and product design to help produce reliable and high quality cast components, and more particularly to working across various size scales as a way to accurately model a cast component in way that is both physically accurate and computationally efficient.
Many critical structural applications utilize cast components or products. This is especially true for automotive and related transportation systems, where engines, transmissions, suspension systems, load-bearing primary structures, seating components, interior support structures or the like have all benefited from the low-cost manufacturing associated with casting. Casting processes are often the most cost effective method to produce geometrically complex components and offer net shape or near net-shape capability in comparison with other manufacturing processes. Such casting processes are especially beneficial when used in conjunction with lightweight structural materials, such as aluminum-based, magnesium-based or related alloys, where high strength to weight ratios, good corrosion resistance, and relatively low raw material cost are useful features.
The relatively recent use of computers and their ability to provide automated control has led to even more efficient casting and related manufacturing processes. Similar advancements in computer-based tools have enabled improvements in component design. Individually, such computer-implemented means are known as computer aided manufacturing (CAM) for processing and computer aided design (CAD) for components, while collectively they are known as part of the broad use of computer software known as computer aided engineering (CAE) that also may include computer-aided analysis (CAA), computer-integrated manufacturing (CIM), computer-aided manufacturing (CAM), material requirements planning (MRP), computer-aided planning (CAP) or the like. Generally CAE takes the design from basic principles from CAD and applies more detailed engineering principles to the intended operating environment. Traditionally, component design and process modeling activities have been conducted relatively independently of one another, with the process modeling work largely taking place only after the component design process is substantially complete. Such independence frequently results in long casting development cycles, as well as less than optimum casting quality, reliability or other indicia of component integrity. Additional complexity arises when other considerations, such as the effect of casting defects and related small scale properties, as well as their impact on product performance, are included in the product and process development cycle.
An even more recent discipline, known as Integrated Computational Materials Engineering (ICME), focuses on employing computer-based tools to improve the development of cast components by linking processes and structures to their corresponding properties to computationally simulate component performance prior to undertaking any actual fabrication-related activities. Despite the advantages associated with ICME, initial simplifying assumptions must still be made with regard to casting design, process modeling and optimization, as well as prediction of defects, microstructure and product performance. Many of these assumptions (for example, uniformity in crystal structure, phase properties, precipitates or the like) are based on inherent component designer or manufacturing engineer experience, trial-and-error iterations and other ad hoc approaches, where the emphasis is instead on prototype and foundry trial troubleshooting that takes place only once certain input parameters (for example, alloys, casting processes, casting and gating system features or the like) have been selected or designed.
Neglecting the effect of variations occurring at the smaller scales of lightweight metal alloy castings manifests itself in inaccuracies in the determination of larger scale constituent properties. Likewise, an attempt that only deals with small scale size variations would not be appropriate for modeling larger structures (such as that associated with an entire engine block in automotive applications), as the scales appropriate for smaller scale (i.e., micrometer or nanometer) area investigation would be a prohibitively unwieldy undertaking if applied to the entire component or related larger scale investigation.
Similarly, disregarding or not properly characterizing the effects of conditions such as microporosity, defect formation or residual stress on fatigue life (especially over multiple scale sizes) would make it hard to accurately characterize component performance. For example, microporosity (which tends to be the most common casting defect) can be a significant problem in casting design where simplified methods are used that estimate the biggest so-called micropore based on the local solidification time. Solidification of the metal often takes place in the form of dendrites (which resemble small pine trees in three-dimensional space). The spacing between the dendrites is a function of the local solidification time, and the largest micropore size can be estimated as roughly proportional to dendrite spacing, often by a factor of two or three. Such an empirical approach may provide reasonable estimates on average, but because microporosity is often interconnected over several dendrites or even dendritic grains, this method does not give very good estimates of part performance. While it is possible to make a statistical estimate of the largest micropore (for example, a Maximum Likelihood Estimate or the like) from the empirically based estimates of the average pore size, such approaches are not as accurate as they could be. Even with systems that make a reasonable estimate of factors such as these, it would be beneficial to analyze a broader scale of defects in order to establish a more physically correct model of the defect formation processes that occur during casting, as well as how these defects and the metal surrounding them respond to the service conditions. While various types of microporosity modeling techniques (such as criterion functions, interdendritic flow models, pore growth models and cellular automata (CA)) have been employed to partially explain aspects of the casting phenomena, none have proven adequate for fully modeling a cast component in all its complexity.
For example, criterion functions are empirical rules that use local solidification conditions (cooling rate, solidification velocity, thermal gradients or the like) to predict microporosity formation. While these models are easy to use, they are not applicable under a full range of operating conditions (pressures and geometry) and are therefore limited in scope, especially as they relate to model prediction accuracy. Interdendritic flow models, which comprise the current state-of-the-art in commercial finite element/finite difference process modeling software, model the liquid flow feeding solidification shrinkage as a flow-through porous medium (colloquially referred to as the mushy zone). The partitioning of hydrogen gas between liquid and solid phases is modeled, while the formation of hydrogen pores between dendrites is also predicted. In interdendritic flow models, pores are usually assumed spherical with a variable size proportional to some microstructural feature, such as the Secondary Dendrite Arm Spacing (SDAS). However, experimentally-recorded pore growth kinetics disagree with those predicted by interdendritic flow models because pore growth is controlled by the rate at which hydrogen can diffuse to the pores, a key factor which is not included in the interdendritic flow models. Thus, while more generally applicable than the criterion functions, interdendritic flow models have a difficult time accurately predicting pore size. Pore growth models were created to address the principal weakness of interdendritic flow models by more accurately predicting pore size during solidification. In the state-of-the-art pore growth model, the thermal model for pore growth during solidification does not calculate pressure; thus, the porosity (diameter and volume fraction) is consistently underpredicted because the effects of the volumetric changes when metal solidifies on the pressure are not considered. The CA technique for microstructure and pore size prediction, while receiving some attention in academia, has yet to be used in an industrial/commercial setting. In such an approach, the formation of individual grains and dendrites is stochastically modeled with growth rates either analytically prescribed or predicted from solute concentration balances. Pore growth can also be modeled within the CA method via a diffusion equation for hydrogen. While the results from CA have been promising, they require an extremely refined mesh size. Where interdendritic flow models can use mesh dimensions of 1 to 10 mm, CA requires mesh dimensions of 1 to 70 μm—three orders of magnitude smaller. As a result, CA is generally applied to casting submodels, using thermal histories predicted from a macromodel on a coarser mesh.
As such, previous attempts to model aluminum casting across multiple scales have not taken full advantage of an integrated approach, especially as they relate to microporosity (without having to make simplifying assumptions), casting geometry and gating/riser design optimization, treatment of larger defects (such as oxide films, core gas, entrained gas, eutectic phases (including their impact on fatigue calculations)), as well as how to estimate fatigue properties when there are no casting defects present in a particular location.